Cell Fracture, How can I use it properly?
Inspect and Repair your Model




Avoid Overlapping Faces. Avoid Intersecting Faces. All submeshes closed.
Both Meshes have the same number of vertices. 


Yellow CubeFit mesh is free from defects. 
Blue CubeNotFit has overlapping connected submeshes seen in edit mode. Intersecting Faces. This is a defect which can be corrected.






Cell Fractures in next layer.  


CubeFit Succeeds. 
CubeNotfit Fails to retain shape.







Three crude letter (O)s in 3D , first two same mesh, different colors.  Mesh on left has imperfections. Overlapping faces that are difficult to see by casual inspection. Middle Blue Mesh has imperfect overlapping faces, made easy to see by display feature.  Cell Fracture objects on right are the result of an imperfect Cell Fracture on the Middle object.  This flawed result  should not surprise us since we know the source mesh had flaws.  There is no guarantee you will see a flawed result.

Inspect and  correct your mesh to be more like the CubeFit mesh.


If your model is in one piece, archive your file. Break one model into many convenient, not difficult pieces, to see which sub mesh fails. 
As stated in the first comment ...  Menu/Select by All Trait/Non Manifold .. Loose Geometry may reveal defects.